West number
Encyclopedia
The West number is an empirical parameter used to characterize the performance of Stirling engine
s, and other Stirling systems. It is very similar to the Beale number
where a larger number indicates higher performance; however, the West number includes temperature compensation. The West number is often used to approximate of the power
output of a Stirling engine. The average value is (0.25) http://www.ornl.gov/~webworks/cppr/y2001/rpt/27113.pdf for a wide variety of engines, although it may range up to (0.35) http://www.bekkoame.ne.jp/~khirata/academic/simple/simplee.htm, particularly for engines operating with a high temperature
differential.
The West number may be defined as:
where:
When the Beale number is known, but the West number is not known, it is possible to calculate it. First calculate the West number at the temperatures TH and TK for which the Beale number is known, and then use the resulting West number to calculate output power for other temperatures.
To estimate the power output of a new engine design, nominal values are assumed for the West number, pressure, swept volume and frequency, and the power is calculated as follows:
For example, with an absolute temperature ratio of 2, the portion of the equation representing temperature correction equals 1/3. With a temperature ratio of 3, the temperature term is 1/2. This factor accounts for the difference between the West equation, and the Beale equation in which this temperature term is taken as a constant. Thus, the Beale number is typically in the range of 0.10 to 0.15, which is about 1/3 to 1/2 the value of the West number.
Stirling engine
A Stirling engine is a heat engine operating by cyclic compression and expansion of air or other gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work....
s, and other Stirling systems. It is very similar to the Beale number
Beale number
In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power output of a Stirling engine design...
where a larger number indicates higher performance; however, the West number includes temperature compensation. The West number is often used to approximate of the power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
output of a Stirling engine. The average value is (0.25) http://www.ornl.gov/~webworks/cppr/y2001/rpt/27113.pdf for a wide variety of engines, although it may range up to (0.35) http://www.bekkoame.ne.jp/~khirata/academic/simple/simplee.htm, particularly for engines operating with a high temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
differential.
The West number may be defined as:
where:
- Wn is the West number
- Wo is the power output of the engine (wattWattThe watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s) - P is the mean averageArithmetic meanIn mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
gas pressurePressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
(PaPascal (unit)The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
) or (MPaMPA-Academic degrees:* Master of Professional Accountancy* Master of Public Administration* Master of Public Affairs* Master of Physician's Assistant-Chemicals:* Medroxyprogesterone acetate, also known by the brand name Depo-Provera* Morpholide of pelargonic acid...
, if volume is in cm3) - V is swept volumeVolumeVolume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
of the expansion space (m3) or (cm³, if pressure is in MPa) - f is the engine cycle frequencyFrequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
(HzHertzThe hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
) - TH is the absolute temperatureTemperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of the expansion space or heaterHeaterA heater is an object that emits heat or causes another body to achieve a higher temperature. In a household or domestic setting, heaters are usually appliances whose purpose is to generate heating...
(kelvinKelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
s) - TK is the absolute temperature of the compression space or cooler (kelvins)
- Bn is the Beale numberBeale numberIn mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power output of a Stirling engine design...
for an engine operating between temperatures TH and TK
When the Beale number is known, but the West number is not known, it is possible to calculate it. First calculate the West number at the temperatures TH and TK for which the Beale number is known, and then use the resulting West number to calculate output power for other temperatures.
To estimate the power output of a new engine design, nominal values are assumed for the West number, pressure, swept volume and frequency, and the power is calculated as follows:
For example, with an absolute temperature ratio of 2, the portion of the equation representing temperature correction equals 1/3. With a temperature ratio of 3, the temperature term is 1/2. This factor accounts for the difference between the West equation, and the Beale equation in which this temperature term is taken as a constant. Thus, the Beale number is typically in the range of 0.10 to 0.15, which is about 1/3 to 1/2 the value of the West number.